Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

How many different triangles can you make on a circular pegboard that has nine pegs?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you find all the different ways of lining up these Cuisenaire rods?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

What happens when you try and fit the triomino pieces into these two grids?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

My coat has three buttons. How many ways can you find to do up all the buttons?

Can you find out in which order the children are standing in this line?

Try this matching game which will help you recognise different ways of saying the same time interval.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?